What type of food do you like? There is just about any cuisine from around the world. My personal favorite is Ahan (
https://ahanmadison.com/) which is off Capital Square on the side away from campus. Very close to there is also Sardine, which is more of an upscale Bistro but with great views of Lake Monona, but on State Street, there are a ton of options that are going to range from decent quick food to really good and interesting. One of the older places around is Porta Bella, an Italian place just off State Street.
Of course, everyone has to have a brat from State Street Brats and ice Cream on the Union Terrace.